Solve the following heat equation and write the solution as u(x, t) PDE: Ut = Uxx BCs: ux(0, t) = 0, ux(n,t) = 10 IC: u(x, 0): = 10x² 2π

Q: 1. Find the solution of the IVP: x' 13 = - (-43)* -1 5 x (0) ») = (-3).

A: Given that the initial value problem x'=13-15x   ,  x0=-24 This is in the form x'=Ax Here  A=13-15

Q: 2 calculate J= e dyok 2x

A: Given integral :

Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…